Computer-aided engineering analysis (CAE) has been used for assisting engineers/scientists for the past decades in designing products. One of the most popular CAE is finite element analysis (FEA), which is a computerized method widely used in industry to model and solve engineering problems relating to complex systems such as three-dimensional non-linear structural design and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. With the advent of the modern digital computer, FEA has been implemented as FEA software. Basically, the FEA software is provided with a model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are referred to as finite elements. The vertices of the finite elements are referred to as nodes. The model is comprised of a finite number of finite elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA software then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment is created.
Weaving/braiding is a dynamic process, where strings (i.e., yarns, wires, etc.) are drawn from several thread rolls and then bound together in a specific pattern. Similar to many other engineering tasks, CAE (e.g., FEA) has been used for designing such a weaving machine. In particular, simulated physical behaviors of a string being drawn out of a yarn feeder are obtained in a time-marching simulation using a CAE software. One of the shortcomings in prior art approaches is to require the entire yarn in the thread roll be modeled as a large number of finite elements (e.g., truss elements). As a result, it is not only tedious to create such a computerized model, but also inefficient in the numerical simulation thereafter due to the inclusion of many inactive elements located on the thread roll (i.e., only elements near braiding/weaving operations are important for obtaining the simulated physical behaviors).
It would therefore be desirable to have improved methods and systems for numerically simulating physical behaviors of a string drawn out of a yarn feeder in a weaving/braiding machine.